Question
Find the derivative of the function. \[ f(t)=88^{t^{3}} \] \( f^{\prime}(t)=\square \)
Ask by Bolton Griffiths. in the United States
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The derivative of \( f(t) = 88^{t^3} \) is \( f'(t) = 3t^2 \ln(88) \cdot 88^{t^3} \).
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
Like
Extra Insights
To find the derivative of the function \( f(t) = 88^{t^3} \), we can use the chain rule and the exponential rule. The derivative of \( a^u \) is given by \( a^u \ln(a) \cdot u' \). Here, \( u = t^3 \) and \( u' = 3t^2 \). So, we have: \[ f'(t) = 88^{t^3} \ln(88) \cdot 3t^2 = 3t^2 \cdot 88^{t^3} \ln(88). \] Thus, the derivative is: \[ f'(t) = 3t^2 \cdot 88^{t^3} \ln(88). \] Happy differentiating!